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AGA Report No. 3
ORIFICE METERING OF NATURALGAS AND OTHER RELATED
HYDROCARBON FLUIDS
Part 3 Natural Gas Application
American Gas Association and AmericanPetroleum Institute 1992, 2003
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Symbols and Units
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Practical Orifice Flow Equation
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Mass Flow
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EQUATIONS FOR MASS FLOW OF
NATURAL GAS
The equations for the mass flow of natural
gas, in pounds mass per hour
The mass flow developed from the density of
the flowing fluid is expressed as :
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Mass flow developed from the ideal gas
relative density (specific gravity) expressed as
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The mass flow equation developed from real
gas relative density (specific gravity)
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EQUATIONS FOR VOLUME FLOW OF
NATURAL GAS
The volume flow rate of natural gas, in cubic
feet per hour at base conditions
The volume flow rate at base conditions, Qb,
developed from the density of the fluid at
flowing conditions and base conditions
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The volume flow rate at base conditions,
developed from ideal gas relative density
(specific gravity)
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the volume flow rate at base conditions,
developed from real gas relative density
(specific gravity)
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Standard Conditions
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The volume flow rate at standard conditions,
developed from the density of the fluid at
flowing conditions and standard conditions
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The volume flow rate at standard conditions,
developed from ideal gas relative density
(specific gravity)
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the volume flow rate at standard conditions,
developed from real gas relative density
,(specific gravity
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VOLUME CONVERSION FROM
STANDARD TO BASE CONDITIONS
If base conditions are different from standard
conditions, the volume flow rate calculated at
standard conditions can be converted to the
volume flow rate at base conditions throughthe following relationship
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Additional Computation
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DIAMETER RATIO
The diameter ratio ()
the ratio of the orifice bore diameter (d)t o the internal
diameter of the meter tube (0)
used in determining (a) the orifice plate coefficient of discharge,
(b) the velocity of approach factor
(c) the expansion factor
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COEFFICIENT OF DISCHARGE FOR
FLANGE-TAPPED ORIFICE METER
The coefficient of discharge for a flange-tappedorifice meter has been determined from testdata.
It has been correlated as a function of diameterratio (), tube diameter, and pipe Reynoldsnumber
The equation for the concentric, square-edged
flange-tapped orifice meter coefficient ofdischarge developed by Reader-Harris andGallagher
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Reader-Harris/Gallagher equation
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VELOCITY OF APPROACH FACTOR
mathematical expression that relates the
velocity of the flowing fluid in the orifice
meter approach section (upstream meter
tube) to the fluid velocity in the orifice platebore
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REYNOLDS NUMBER
The pipe Reynolds number (ReD) is used as a
correlation parameter to represent the change
in the orifice plate coefficient of discharge
with reference to the meter tube diameter,the fluid flow rate, the fluid density, and the
fluid viscosity
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=0.0000069 pounds mass per-foot-second
Standard Condition Tb = 519.67R, Pb = 14.73
psi, Zbair=0.999590
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If the fluid being metered has a viscosity,
temperature, or real gas relative density
(specific gravity) quite different from those
shown above, the assumptions are notapplicable.
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EXPANSION FACTOR
When a gas flows through an orifice, the changein fluid velocity and static pressure isaccompanied by a change in the density, and afactor must be applied to the coefficient to adjustfor this change.
The factor is known as the expansion factor
The expansion factor (Y) is a function of diameter
ratio, the ratio of differential pressure to staticpressure at the designated tap, and the isentropicexponent (k).
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Compressible Fluid Isentropic
Exponent
The real compressible fluid isentropic exponent,kr is a function of the fluid and the pressure andtemperature.
For an ideal gas, the isentropic exponent, ki, is
equal to the ratio of the specific heats (cp/cv) ofthe gas at constant pressure (cp) and constantvolume (cv) and is independent of pressure.
A perfect gas is an ideal gas that has constant
specific heats. The perfect gas isentropic exponent, kr is equal to
ki evaluated at base conditions
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It has been found that for many applications, the
value of kr is nearly identical to the value of ki,
which is nearly identical to kp. From a practical
standpoint, the flow equation is not particularlysensitive to small variations in the isentropic
exponent.
The perfect gas isentropic exponent, kp, is oftenused in the flow equation. Accepted practice for
natural gas applications is to use kp = k = 1.3.
The application of the expansion factor is valid
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The application of the expansion factor is valid
as long as the following dimensionless
criterion for pressure ratio is followed:
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Expansion Factor Referenced to
Upstream Pressure
If the absolute static pressure is taken at theupstream differential pressure tap, the value
of the expansion factor, Y:
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Expansion Factor Referenced to
Downstream Pressure
If the absolute static pressure is taken at the
downstream differential tap
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Compressibility Ideal and Real Gas
The terms ideal gas and real gas are used to
dene calculation or interpretation methods.
An ideal gas is one that conforms to the
thermodynamic laws of Boyle and Charles
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All gases deviate from the ideal gas laws to
some extent. This deviation is known as
compressibility and is denoted by the symbol
Z.
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Volume Base
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Compressibility at Base Condition
The value of Z at base conditions ( z b ) is
required and is calculated from the
procedures in A.G.A. Transmission
Measurement Committee Report No. 8.
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Supercompressibility
In orifice measurement, z b and 2, appear as a
ratio to the 0.5 power.
This relationship is termed the
supercompressibility factor and may be
calculated from the following equation
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RELATIVE DENSITY
The relative density (specific gravity) is
defined as a dimensionless number that
expresses the ratio of the density of the
flowing fluid to the density of a reference gasat the same reference conditions of
temperature and pressure.
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Ideal Gas Relative Density
The ideal gas relative density (specific gravity),Gi, is defined as the ratio of the ideal densityof the gas to the ideal density of dry air at the
same reference conditions of pressure andtemperature.
Since the ideal densities are defined at thesame reference conditions of pressure and
temperature, the ratio reduces to a ratio ofmolar masses (molecular weights).
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the ideal gas relative density (specific gravity)
is set forth in the following equation:
R l G R l ti D it (R l S ifi
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Real Gas Relative Density (Real Specific
Gravity)
Real gas relative density (specific gravity), Gr, isdefined as the ratio of the real density of the gasto the real density of dry air at the samereference conditions of pressure and
temperature To correctly apply the real gas relative density
(specific gravity) to the flow calculation, thereference conditions for the determination of the
real gas relative density (specific gravity) must bethe same as the base conditions for the flowcalculation.
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At reference (base) conditions (Pb, Tb), real
gas relative density (specific gravity) is
expressed as
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DENSITY OF FLUID AT FLOWING
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DENSITY OF FLUID AT FLOWING
CONDITIONS
The flowing density is a key component ofcertain flow equations.
defined as the mass per unit volume at
flowing pressure and temperature and ismeasured at the selected static pressure taplocation
The value for flowing density can becalculated from equations of state or from therelative density (specific gravity) at theselected static pressure tap.
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The fluid density at flowing conditions can also bemeasured using commercial densitometers.
Most densitometers, because of their physicalinstallation requirements and design, cannot
accurately measure the density at the selectedpressure tap location.
the fluid density difference between the densitymeasured and that existing at the defined pressure
tap location must be checked to determine whetherchanges in pressure or temperature have an impacton the flow measurement uncertainty
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Density Based on Gas Composition
When the composition of a gas mixture is
known, the gas densities t,p and pb may be
calculated from the gas law equations
The molecular weight of the gas may be
determined from composition data, using
mole fractions of the components and their
respective molecular weights
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Density Based on Ideal Gas Relative
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Density Based on Ideal Gas Relative
Density (Specific Gravity)
The following equations are applicable when a
gas analysis is available:
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Density Based on Real Gas Relative
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Density Based on Real Gas Relative
Density
The relationship of real gas relative density
(specific gravity) to ideal gas relative density
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INSTRUMENT CALIBRATION
Calibration standards for differential pressure
and static pressure instruments are often
used in the field without local gravitational
force adjustment or correction of the valuesindicated by the calibrating standards.
The manometer readings are affected by local
gravitational effects, water temperatures, andthe use of other than distilled water.
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Pressure devices that employ weights are also
used to calibrate differential pressure
instruments without correction for the local
gravitational force. Deadweight testers are used to calibrate static
pressure measuring equipment without
correction for the local gravitational force.
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It is usually more convenient and accurate toincorporate these adjustments in the flowcomputation than for the person calibrating theinstrument to apply these small corrections
during the calibration process. Therefore, additional factors are added to the
flow equation for the purpose of including theappropriate calibration standard corrections in
the flow computation either by the flowcalculation procedure in the office or by themeter technician in the field
Six factors are provided that may be used
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individually or in combination, depending on
the calibration device and the calibration
procedure used:
Volume flow equation
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Water Manometer Gas Leg Correction
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Water Manometer Gas Leg Correction
Factor (Fam)
The factor Fam corrects for the gas leg over
water when a water manometer is used to
calibrate a differential pressure instrument:
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When atmospheric air is used as the medium
to pressure both the differential pressure
instrument and the water U-tube manometer
during calibration, the density of air atatmospheric pressure and 60F must be
calculated using the following equation:
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